As black: the London System With Colors Reversed

The only reason I can see is answering 6.c4 with 6...Bb4+, when the "natural reaction" 7.Nc3? loses to 7...Qa5.

But then, I do not see why white has to hurry pushing c2-c4.

I’m not saying that the position is winning for black, but black’s game is very comfortable. Your pieces are coordinated and both queenside and kingside attacks are possible. Plus, don’t downplay the fact that it’s very disruptive to the plans of many Nimzo-Larsen players go for. With best play white is equal, but they have to be moves that they usually don’t like to make. For instance, if you retreat the bishop to d6, white’s best move in some positions is often to try to trade it off with Ba3, but I have never seen an N-L player willingly part with that bishop.

Edit: to be fair, though, you're an IM and I stink. The opponents you face are much more likely to be adaptive to the needs of the position than the players that I face, who are much more likely to stick with their usual plans even if they aren't the best.

Maybe, but if you look at the stem position after c6 I think it's pretty obvious that it's black who is playing for advantage. There are no weaknesses and plenty of piece coordination. The position has been reached 125 times in 2500 rated games, and black has won 56% of the time and white only 33%.

I played someone several hundred points higher than myself in a 30|20 to a draw from this position and only because I stupidly allowed a perpetual. Otherwise I was better. I have had a lot of luck with it. It's not a panacea by any means, but it's a solid structure to fight against the rare Nimzo-Larsen opening. I have no desire to learn theory against rare openings if I don't have to.

I'm in my early sixties, and of course I cannot play like an IM now. Say some 150 rating points lower that the limit, and they will be more and more.

5.d4 is Stockfish's #1 choice in the position and the move that gives white the best chance of winning in the Master game database. 5.c4 wins 24% and 5.d4 wins 34%. 5.c4 is much more likely to draw, though. I won't argue about the minutia, but it's clearly not objectively bad, it just doesn't conform to your predispositions.

If you say so. I just think that if Stockfish says it's best and white wins with it the most, then it's not objectively bad. Notice that I did not say that it was the best move, I just presented a couple of nuggets and said it wasn't bad. The definition of objective is that it's not infuenced by personal opinion or feelings, and to my knowledge Stockfish doesn't any feelings about anything. You don't like it—that's clear and that's fine. I won't argue with you.